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Showing posts with the label Logarithmic spiral

Fractal Koch Snowflake Spiral

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The Koch Snowflake Spiral 2024: last year, I published, using the following, an interpretation of Quantum Mechanics. https://www.fractalnomics.com/2023/05/fractal%20foundational%20quantum%20theory%20published%20.html International Journal of Quantum Foundations, Speculations. The Fractal Corresponds with Light and Foundational Quantum Problems   Experiment on Inverted Fractal Corresponds with Cosmological Observations and Conjectures On route to understanding if  fractals have a 'wavy' like nature , I finally put pencil to paper and drew what I'd been thinking. I have been pondering what effect a 'mutation' or change to one triangle - a dot at the apex of the triangle as shown below - would have or show on the  iterating  Koch Snowflake. I envisaged that it would spiral to infinity, as shown below. By tracing a smooth curve through the (red) 'dots' series of iterated mutant triangles, I would develop - what looks like - a kind of logarith...

Fractal: Wave Particle Duality

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  I have since published in 2023:  This entry is one of a set of entries on the fractal and their strange (quantum-like) nature. I use the word quantum because no other area of knowledge comes close to explaining or relating to the discoveries I am making with fractal geometry. Blair 11,03,2013 Wave and particle D uality - and the fractal The entry below is a discovery, not an explanation. I (intend to) write what I see and what I expect I have found— I do not pretend to fully understand. Just as the atom can ' weirdly' be described as being both a particle and as a ‘smeared out’ wave at the same time, so too, as I shall demonstrate, can the fractal be described in such a way  - only for the fractal it is not so weird. The fractal demonstrating a (discrete) particle: The fractal is defined by  a pattern, object or shape  repeating or iterating. The Koch Snowflake (below) demonstrates this iterating - the triangle re...